Estimates the probabilities of price changes, Mathematics

Mr. Hoper is in charge of investments for the golden horizon company. He estimates from past price fluctuations in the gold market that the probabilities of price changes on a given day are dependent upon price changes on the previous day. If gold price increases or remains constant, the following distribution represents the probability of price changes in $ per ounce for the day to follow:

Price change ($) Probability

-4 0.05

-2 0.10

No change 0.20

+2 0.25

+4 0.30

+6 0.10

On the other hand, if gold prices reduces on a given day, the next day's distribution of price changes in $ per ounce is:

Price change ($) Probability

-6 0.10

-4 0.30

-2 0.25

No change 0.15

+2 0.20

Test the policy of buying 100 ounces when prices drop for the preceeding three days and selling 100 ounces when prices rise for the preceding three days.

Simulate for thirty days. Assume at the start that mr. hoper has 1000 ounce of gold for which he has paid $300 per ounce. Determine how much gold will he own at the end of thirty days, as well as his net profit/loss position during this period. Assume at the start that gold is selling at $300 per ounce and that during the day before start of simulation, gold prices rose.